Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x+6y &= -6 \\ -x+8y &= 2\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-x = -8y+2$ Divide both sides by $-1$ to isolate $x$ $x = {8y - 2}$ Substitute this expression for $x$ in the first equation. $-2({8y - 2}) + 6y = -6$ $-16y + 4 + 6y = -6$ Simplify by combining terms, then solve for $y$ $-10y + 4 = -6$ $-10y = -10$ $y = 1$ Substitute $1$ for $y$ in the top equation. $-2x+6( 1) = -6$ $-2x+6 = -6$ $-2x = -12$ $x = 6$ The solution is $\enspace x = 6, \enspace y = 1$.